The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  2  2 2a 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2a+2  2 2a^2+2a+2 2a^2+2  0 2a 2a^2+2a+2 2a 2a^2+2a+2 2a^2+2a  0 2a 2a 2a^2 2a  2 2a^2+2a 2a^2  2 2a+2 2a^2+2 2a^2+2a  0  0 2a^2 2a^2+2a 2a^2 2a^2+2 2a^2 2a+2  2 2a+2 2a^2+2a+2  2  0 2a^2+2 2a^2 2a^2+2a+2 2a^2 2a^2+2a 2a^2  2 2a 2a^2 2a 2a^2+2a+2 2a^2+2a 2a^2+2a 2a 2a+2 2a 2a^2 2a 2a+2 2a^2+2a 2a^2+2a+2  0  0  2 2a^2 2a^2+2  0  0 2a^2  0  2
 0  0  2  0 2a^2+2 2a^2+2a+2 2a 2a^2+2 2a^2+2 2a 2a^2+2 2a^2 2a 2a+2  2 2a^2+2a+2  2  2 2a^2+2a  2 2a+2 2a 2a^2+2a  0 2a^2  0  0 2a^2 2a^2 2a^2+2  2 2a^2+2a+2 2a^2+2a 2a^2+2 2a^2  2  0 2a^2+2 2a^2 2a^2+2a+2  0  2 2a^2+2a+2 2a^2+2a+2 2a 2a^2+2a 2a^2+2 2a^2  2  0 2a^2+2a+2 2a^2+2a+2 2a 2a^2+2a 2a^2+2  0  0 2a^2+2a 2a^2+2a+2 2a^2+2a+2 2a^2+2 2a^2+2a 2a^2+2  0 2a^2+2a 2a^2 2a^2 2a^2 2a 2a+2 2a^2+2a 2a  2 2a^2+2  0 2a^2+2a
 0  0  0  2  2 2a^2+2a 2a^2+2a  2 2a^2+2 2a^2+2a 2a^2+2 2a^2+2 2a+2 2a 2a^2+2a 2a 2a+2 2a^2+2a+2 2a^2+2 2a^2+2a 2a^2  2  0 2a^2+2a+2  0 2a^2+2a+2 2a 2a^2+2 2a+2  0 2a+2 2a^2+2 2a+2 2a^2+2a 2a 2a^2  0 2a^2+2a 2a^2  2 2a 2a^2 2a^2+2a+2 2a^2 2a+2 2a+2  0 2a+2 2a^2 2a^2+2a 2a^2+2a+2 2a+2 2a^2+2 2a+2  0 2a^2+2a  0  2 2a^2+2 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2 2a^2+2a  0 2a^2+2 2a^2  2 2a^2+2a 2a+2 2a 2a^2 2a^2+2 2a 2a+2  2

generates a code of length 76 over GR(64,4) who´s minimum homogenous weight is 504.

Homogenous weight enumerator: w(x)=1x^0+308x^504+868x^512+602x^520+609x^528+28672x^532+476x^536+322x^544+245x^552+245x^560+189x^568+98x^576+77x^584+42x^592+7x^600+7x^608

The gray image is a code over GF(8) with n=608, k=5 and d=504.
This code was found by Heurico 1.16 in 0.84 seconds.